Quantum Groupoids and their Hopf Cyclic Cohomology
Abstract
A new quantization of groupoids under the name of ×-Hopf coalgebras is introduced. We develop a Hopf cyclic theory with coefficients in stable-anti-Yetter-Drinfeld modules for ×-Hopf coalgebras. We use ×-Hopf coalgebras to study coextensions of coalgebras. Finally, equivariant ×-Hopf coalgebra Galois coextensions are defined and applied as functors between categories of stable anti-Yetter-Drinfeld modules over ×-Hopf coalgebras involved in the coextension.
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